Why We Irrationally Choose: Unpacking Prospect Theory’s Value & Weight Functions

I recently realized my spending is often irrational, prompting a look at how invisible forces drive economic decisions; Daniel Kahneman and Amos Tversky’s 1979 Prospect Theory offers a compelling framework to quantify such non‑rational behavior.

1 Prospect Theory

Prospect Theory was introduced by Daniel Kahneman and Amos Tversky in 1979 to describe the psychological processes behind risk‑related decisions. The theory consists of two main components: the value function and the weight function .

1.1 Value Function

The value function translates monetary outcomes into psychological utility. It is concave for gains, convex for losses, and steeper in the loss domain, reflecting loss aversion. Mathematically, it captures two phenomena: loss aversion and risk aversion.

Loss aversion means that the pain of a loss outweighs the pleasure of an equivalent gain. Risk aversion is represented by parameters less than one in the gain region, causing diminishing marginal utility as gains increase.

1.2 Weight Function

The weight function describes how people subjectively weight probabilities. Even when probabilities are known, individuals often over‑estimate low‑probability events and under‑estimate high‑probability ones, a phenomenon called probability distortion . The function also accounts for preference reversal , where risk preferences switch at different probability levels.

1.3 Integrated Model

In Prospect Theory, overall expected utility is calculated by multiplying each outcome’s value by its subjective weight, rather than by the objective probability.

The theory has been widely applied in finance, insurance, gambling, and marketing to explain behaviors such as over‑trading, the disposition effect, and excessive insurance purchase.

2 Application Example: Investment Decision

Consider an investor choosing between a risky investment A (with a certain probability of gain and loss) and a safe investment B (no gain, no loss). Using assumed value and weight functions, the expected utility of A is negative (≈‑136.42) while B’s is zero, leading the investor to prefer B despite its lack of positive return—illustrating loss aversion and probability weighting.

3 Prospect Theory vs. Traditional Economic Theory

3.1 Expected Utility Theory

Traditional expected utility theory assumes rational agents who maximize the weighted sum of outcomes using objective probabilities. In the same investment example, it predicts choosing A because its expected monetary value is positive.

3.2 Prospect Theory

Prospect Theory incorporates loss aversion and nonlinear probability weighting, predicting the choice of B, which aligns better with observed behavior. Empirical studies repeatedly show Prospect Theory’s superior predictive power in real‑world decisions.

Below are illustrative graphs comparing the value and weight functions of Prospect Theory with the linear functions of traditional theory.

The left graph shows the concave gain and convex loss shapes of Prospect Theory’s value function, highlighting steep loss aversion, while the traditional linear function lacks these features. The right graph displays the nonlinear weighting curve of Prospect Theory, illustrating the tendency to over‑estimate low probabilities and under‑estimate high probabilities, contrasted with the linear weighting of expected utility theory.

Overall, Prospect Theory provides a powerful lens for understanding and predicting human behavior in risky situations, offering insights that extend beyond finance to marketing, insurance, and everyday decision‑making.